Hi,
I am not too familiar with either of these schools, but I know about Latin American studies. I graduated from the MA program at Georgetown, along with a bunch of journalists.
Even though Gtown has a pretty amazing career center and excellent internship placements, in the end what got me my internships and my job was the name of the school, the people I met while I was a student (everyone likes to meet students, it turns out) and the city where the school is located. Applying this to your problem, I would go to NYU. I think NYC is likely to offer you better opportunities than Chicago can and I think a 2-year program will give you more flexibility to intern while you go to school.
Lastly don't worry too much about funding. I was accepted with zero funding and by the second year had full tuition remission plus a stipend and an internship. Best decision I ever made in my life.
Buena suerte!